Answered: Ball Pull Disk

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Ball Pull Disk

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Question

A disk of radius 25.0 cm is free to turn about an axle
perpendicular to it through its center. It has very thin but strong string
wrapped around its rim, and the string is attached to a ball that is pulled
tangentially away from the rim of the disk (Fig. ). The pull increases
in magnitude and produces an acceleration of the ball that obeys the equation
a1t2 = At, where t is in seconds and A is a constant. The cylinder
starts from rest, and at the end of the third second, the ball’s acceleration
is 1.80 m/s2. (a) Find A. (b) Express the angular acceleration of the disk
as a function of time. (c) How much time after the disk has begun to turn
does it reach an angular speed of 15.0 rad/s? (d) Through what angle has
the disk turned just as it reaches 15.0 rad/s?

Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .

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